1429edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 2265 -1429 }}
| {{monzo| 2265 -1429 }}
| {{mapping| 1429 2265 }}
| {{mapping| 1429 2265 }}
| -0.0235
| &minus;0.0235
| 0.0234
| 0.0234
| 2.80
| 2.80
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| {{monzo| 39 -29 3 }}, {{monzo| -66 -36 53 }}
| {{monzo| 39 -29 3 }}, {{monzo| -66 -36 53 }}
| {{mapping| 1429 2265 3318 }}
| {{mapping| 1429 2265 3318 }}
| -0.0114
| &minus;0.0114
| 0.0257
| 0.0257
| 3.06
| 3.06
Line 41: Line 33:
| 4375/4374, {{monzo| 26 4 -3 -14 }}, {{monzo| 40 -22 -1 -1 }}
| 4375/4374, {{monzo| 26 4 -3 -14 }}, {{monzo| 40 -22 -1 -1 }}
| {{mapping| 1429 2265 3318 4012 }}
| {{mapping| 1429 2265 3318 4012 }}
| -0.0302
| &minus;0.0302
| 0.0395
| 0.0395
| 4.70
| 4.70
Line 48: Line 40:
| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
| {{mapping| 1429 2265 3318 4012 4944 }}
| {{mapping| 1429 2265 3318 4012 4944 }}
| -0.0471
| &minus;0.0471
| 0.0488
| 0.0488
| 5.81
| 5.81
Line 55: Line 47:
| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
| {{mapping| 1429 2265 3318 4012 4944 5288 }}
| {{mapping| 1429 2265 3318 4012 4944 5288 }}
| -0.0420
| &minus;0.0420
| 0.0460
| 0.0460
| 5.48
| 5.48
Line 62: Line 54:
| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
| {{mapping| 1429 2265 3318 4012 4944 5288 5841 }}
| {{mapping| 1429 2265 3318 4012 4944 5288 5841 }}
| -0.0364
| &minus;0.0364
| 0.0447
| 0.0447
| 5.32
| 5.32
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio
! Temperaments
|-
|-
| 1
| 1
Line 87: Line 73:
| 25/18
| 25/18
| [[Trillium]]
| [[Trillium]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Scales ==
== Scales ==
Line 95: Line 81:
== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] | [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] | [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning
* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] | [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] | [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] &ndash; gross in 1429edo tuning


[[Category:Listen]]
[[Category:Listen]]

Revision as of 04:02, 16 November 2024

← 1428edo 1429edo 1430edo →
Prime factorization 1429 (prime)
Step size 0.839748 ¢ 
Fifth 836\1429 (702.029 ¢)
Semitones (A1:m2) 136:107 (114.2 ¢ : 89.85 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

1429edo has a reasonable approximation of the full 17-limit. It is consistent to the 9-odd-limit with only 11/10 barely missing the line. The 11-limit optimal tuning of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.

The equal temperament tempers out 4375/4374 in the 7-limit; 131072/130977, 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; 2080/2079, 4096/4095, 4225/4224, 78125/78078, and 123201/123200 in the 13-limit; 2500/2499, 5832/5831, 11016/11011, and 12376/12375 in the 17-limit. It supports the gross temperament and provides the optimal patent val for the 11- and 13-limit trillium temperament.

Prime harmonics

Approximation of prime harmonics in 1429edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.074 -0.030 +0.243 +0.397 +0.060 +0.013 -0.242 -0.143 -0.046 +0.381
Relative (%) +0.0 +8.9 -3.5 +29.0 +47.2 +7.2 +1.6 -28.8 -17.0 -5.5 +45.3
Steps
(reduced) 		1429
(0) 		2265
(836) 		3318
(460) 		4012
(1154) 		4944
(657) 		5288
(1001) 		5841
(125) 		6070
(354) 		6464
(748) 		6942
(1226) 		7080
(1364)

Subsets and supersets

1429edo is the 226th prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [2265 -1429⟩ | [⟨1429 2265]] | −0.0235 | 0.0234 | 2.80 |- | 2.3.5 | [39 -29 3⟩, [-66 -36 53⟩ | [⟨1429 2265 3318]] | −0.0114 | 0.0257 | 3.06 |- | 2.3.5.7 | 4375/4374, [26 4 -3 -14⟩, [40 -22 -1 -1⟩ | [⟨1429 2265 3318 4012]] | −0.0302 | 0.0395 | 4.70 |- | 2.3.5.7.11 | 4375/4374, 131072/130977, 759375/758912, 3294225/3294172 | [⟨1429 2265 3318 4012 4944]] | −0.0471 | 0.0488 | 5.81 |- | 2.3.5.7.11.13 | 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172 | [⟨1429 2265 3318 4012 4944 5288]] | −0.0420 | 0.0460 | 5.48 |- | 2.3.5.7.11.13.17 | 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045 | [⟨1429 2265 3318 4012 4944 5288 5841]] | −0.0364 | 0.0447 | 5.32 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 109\1429 | 91.533 | [144 -22 -47⟩ | Gross |- | 1 | 674\1429 | 565.990 | 25/18 | Trillium Template:Rank-2 end Template:Orf

Scales

Music

Francium
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